U mdp@s6dZddlZddlmZd ddZGdd d eZdS) zc Extreme Value Copulas Created on Fri Jan 29 19:19:45 2021 Author: Josef Perktold License: BSD-3 N)Copulac Cs>|\}}tt|||t|t||f|S)z+generic bivariate extreme value copula )npexplog)u transformargsvrrg/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/distributions/copula/extreme_value.py copula_bv_evsr csZeZdZdZdfdd ZddZddd Zdd d Zdd d ZdddZ ddZ Z S)ExtremeValueCopulaaSExtreme value copula constructed from Pickand's dependence function. Currently only bivariate copulas are available. Parameters ---------- transform: instance of transformation class Pickand's dependence function with required methods including first and second derivatives args : tuple Optional copula parameters. Copula parameters can be either provided when creating the instance or as arguments when calling methods. k_dim : int Currently only bivariate extreme value copulas are supported. Notes ----- currently the following dependence function and copulas are available - AsymLogistic - AsymNegLogistic - AsymMixed - HR TEV and AsymBiLogistic currently do not have required derivatives for pdf. See Also -------- dep_func_ev rcs6tj|d||_|j|_||_|dkr2tddS)N)k_dimrz(Only bivariate EV copulas are available.)super__init__r Zk_argsr ValueError)selfr r r __class__rr r6s zExtremeValueCopula.__init__cCs>t|tjrt|}|dks$|dkr*|j}t|ts:|f}|S)Nr) isinstancerZndarraytupler )rr rrr _handle_args>s  zExtremeValueCopula._handle_argsc CsVt|j\}}||}tt|||jt|t||f|}|S)aJEvaluate cdf of bivariate extreme value copula. Parameters ---------- u : array_like Values of random bivariate random variable, each defined on [0, 1], for which cdf is computed. Can be two dimensional with multivariate components in columns and observation in rows. args : tuple Required parameters for the copula. The meaning and number of parameters in the tuple depends on the specific copula. Returns ------- CDF values at evaluation points. )rasarrayTrrrr )rrr r Zcdfvrrr cdfJs  "zExtremeValueCopula.cdfc Cs|j}t|j\}}||}t||}t||}|||}||f|} |j|f|} |j|f|} |||| d|| | || | d|||} | S)aJEvaluate pdf of bivariate extreme value copula. Parameters ---------- u : array_like Values of random bivariate random variable, each defined on [0, 1], for which cdf is computed. Can be two dimensional with multivariate components in columns and observation in rows. args : tuple Required parameters for the copula. The meaning and number of parameters in the tuple depends on the specific copula. Returns ------- PDF values at evaluation points. r) r rrrrrrZderivZderiv2) rrr tru1u2Zlog_u12trdepZd1Zd2Zpdf_rrr pdfcs  $zExtremeValueCopula.pdfcCst|j||dS)aREvaluate log-pdf of bivariate extreme value copula. Parameters ---------- u : array_like Values of random bivariate random variable, each defined on [0, 1], for which cdf is computed. Can be two dimensional with multivariate components in columns and observation in rows. args : tuple Required parameters for the copula. The meaning and number of parameters in the tuple depends on the specific copula. Returns ------- Log-pdf values at evaluation points. )r )rrr"rrr rrr logpdfszExtremeValueCopula.logpdfcCstdS)uconditional distribution not yet implemented C2|1(u2|u1) := ∂C(u1, u2) / ∂u1 = C(u1, u2) / u1 * (A(t) − t A'(t)) where t = np.log(v)/np.log(u*v) NNotImplementedErrorr#rrr conditional_2g1s z"ExtremeValueCopula.conditional_2g1cCstdS)Nr%)rdatarrr fit_corr_paramsz!ExtremeValueCopula.fit_corr_param)rr)r)r)r)r) __name__ __module__ __qualname____doc__rrrr"r$r'r) __classcell__rrrr rs   !  r)r)r-numpyrZcopulasrr rrrrr s